What is the domain of f(x)=(3-sqrt(x^2-7))/(x-4) ?

The domain of f(x)=(3-sqrt(x^2-7))/(x-4) is x 4

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domain of f(x)=(3-sqrt(x^2-7))/(x-4)

domain

f (x) = \frac{3 - x ^{2} - 7}{x - 4}

x \leq - 7 or 7 \leq x < 4 or x > 4

Interval Notation

(- \infty, - 7] \cup [7, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 7 or x \geq 7

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq - 7 or 7 \leq x < 4 or x > 4

f (x) = \frac{x + 2}{x ^{2} + 1}

y = - 2 tan (2 θ) + 1

f (x) = \frac{4 x - 5}{x + 6}

f (x) = \frac{2 x}{x ^{2}}

(\frac{5}{6})^{\frac{x ^{2} - 3 x}{x ^{2}}}

What is the domain of f(x)=(3-sqrt(x^2-7))/(x-4) ?
The domain of f(x)=(3-sqrt(x^2-7))/(x-4) is x<=-sqrt(7)\lor sqrt(7)<= x<4\lor x>4